Strange I have never had that problem. The elements will not move relative to each other as long as the playhead is positioned at the end of each timeline when Paste is used.
If you would rather, there is a less graphically confusing method:
Select all the elements in a project's timeline and then select File/New.../ Compound Clip. This will create one fully nameable married unit with all the video, sound & effects and which in turn may be copied and pasted into a new project. One additional good feature of this is that within the newly created Project with a bunch of added Compound Clips, one can select [Right click] Open in Timeline on a single Compound Clip and it will reopen the original timeline to make adjustments - if necessary.